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23 cubits (and a fraction) is the difference in elevation between the Spring of Eitam and the courtyard of the Beis Hamikdash.
The importance of this is that this spring was the source for the Kohen Gadol's mikvah, which was situated atop one of the gates (twenty cubits above the courtyard) and which was three cubits tall. In this way the water could flow into the mikvah based on gravity alone, without requiring pumps or the like, which would disqualify it. (Yoma 31a)